International Patent Publication No. WO 89/05963 describes a mass flow sensor having a membrane. The membrane is composed of a multiplicity of dielectric layers. On the membrane, thin-film resistor elements are arranged which are used to heat the membrane and to measure the temperature of the membrane. The membrane is composed of a plurality of layers which are selected with regard to their thermal expansion coefficients such that slight tensile stresses relative to the silicon frame are enabled to be set. On the upper side of the membrane and of the resistor elements, a covering layer is applied, also made of a dielectric material.